Exact computation of area moments for spline and wavelet curves

We present an exact algorithm for the computation of the moments of a region bounded by a curve represented in a scaling function or wavelet basis. Using Green´s theorem, we show that the computation of the area moments is equivalent to applying a suitable multidimensional filter on the coefficients of the curve and thereafter computing a scalar product. We compare this algorithm with existing methods such as pixel-based approached and approximation of the region by a polygon